Neighborhood systems and their rough sets have robustness and adaptability, and relevant neighborhood information measures underlie uncertainty analysis and intelligent processing. The classical conditional neighborhood entropy becomes fundamental and representative for dependency measurement, but it has three limitations: interaction incompleteness, hierarchy lack, and inconclusive monotonicity/non-monotonicity. This paper aims to improve the conditional neighborhood entropy, and thus we establish three-way neighborhood entropies based on three-level granular structures. At first, three-level...